What is Spatial Concurrent Forces?

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Introduction to Spatial Concurrent Forces

If two or more than two forces are acting on different planes then the forces are known as a System ofNon-CoplanarForces. If these forces act at a common point then they are called as Non-Coplanar Concurrent Forces. The effect of these forces can be determined by combining these forces as a resultant force. Transtutors helps you to understand the concept of spatial concurrent forces.

Spatial Concurrent Forces

In a three dimensional coordinate system, if the lines of action of many forces are intersect at a single point then these forces are called Spatial Concurrent Forces. These forces or the lines of action of these forces do not lie on a single plane. The resultant force of the spatial concurrent forces can be determined as follows:

Determine the resultant force along X, Y and Z directions.

Rx = Σ Fx , Ry = Σ Fy , Rz = Σ Fz

Determine the resultant force of the resultant forces along the three coordinates.

Three Rectangular Components of a Force

If a force F is acting inclined to X, Y and Z axes, then this force can be resolved into three components namely a component along the X-direction (X-component), a component along the Y-direction (Y-component) and a component along the Z-direction (Z-component) as shown in figure.

The unit vectors i, j, and k are in the x-, y-, and z-directions, respectively.

Example of Spatial Concurrent Forces

Example 1:

A force F of 200 N is acting on a bolt as shown in figure. Express the force F in terms of Cartesian vector.

Given: F = 200 N;

Here, the angle between the force and the Y-axis, ß = 60°

The angle between the force and the Z-axis, γ = 45°

The angle between the force and the X-axis, α = ?

We know that,

cos2α+ cos2ß + cos2γ= 1

cos2α + cos260 + cos245 = 1

α = 60°

F = F cos α i + F cos ß j + F cos γk

F (200 cos60)i + (200 cos60)j + (200 cos45)k

F =[100 i + 100 j + 141.4k] N

Example 2:

Two forces of F1 and F2 are acting on an eye bolt as shown in figure. Find the resultant force vector of the system of forces and its magnitude. Also find out the coordinate angles of the forces.

Let us draw the free body diagram of the given system of forces.

The angles α, ß and γ are found out form the components of the unit vectors acting in the direction of the resultant force FR

Example 3:

A load of 600 N is supported by three ropes as shown in figure. Draw the free body diagram and determine the tensions in the rope AB, AC and AD.

Let us draw the free body diagram as shown in figure.

Now equate the respective components of i , j , k to zero.

ΣFx = 0.5 FB – FC + 0.333 FD = 0

ΣFy = 0.866 FB – 0.667 FD = 0

ΣFz = 0.667 FD – 600 = 0

On solving the three equations simultaneously, we get

FC = 646 N

FD = 900 N

FB = 693 N

Engineering Mechanics help site provides you clear understanding of spatial concurrent forces with solves examples.